Download The Real Number System

The Real Number System
Real Numbers
• The set of all rational and the set
of all irrational numbers together
make up the set of real numbers.
• Any and all kinds of numbers fall
under real numbers.
Rational Numbers
Rational numbers are
numbers that can be written
as fractions. That is, the
form a/b where a and b are
both integers and b ≠ 0.
Examples of Rational Numbers
•
•
•
•
-6
8 2/5
.05
-2.6
• 5.3333333
• -8.12121212…
• √16
Irrational Numbers
• Irrational Numbers – numbers that
are not repeating or terminating
decimals.
• Examples:
• .01001000100001…
• √2 = 1.414213562…
• 3.14159…
Whole Numbers, Natural Numbers,
and Integers
• Whole Numbers include the following:
• 0,1,2,3,4,5,6,7,8,9,10,…..
• Natural Numbers include the following:
• 1,2,3,4,5,6,7,8,9,10,….. Does not
include 0.
• Integers include the following:
• …-3,-2,-1,0,1,2,3,…
Classifying Real Numbers
• Directions: Classify the
following numbers as
natural, whole, integer,
rational, and/or irrational.
•8
• This number is a natural number, a
whole number, an integer, and a rational
number.
• 0.33333
• This repeating decimal is a rational
number because it is equivalent to 1/3.
• √17
• √17 = 4.123105… It is not the square
root of a perfect square so it is irrational.
• -28/2
• Since -28/4 = -14, this number is
an integer and a rational number.
• -√121
• Since -√121 = -11, this number is
an integer and a rational number.
Solving Equations
• a2 = 49
• To undo the square, take the square
root of both sides. Then, you have
this.
• √a2 = √49
• a = √49 or a = -√49
• a = 7 or a = -7
• Hence, the solutions are 7 and -7.
•
•
•
•
•
•
d2 = 55
Take the square root of both sides.
√d2 = √55
d = √55 or d = - √55
d = 7.41 or d = - 7.41
Hence, the solutions are 7.41 and
-7.41.